LMFDB - Embedded newform 675.2.k.b.424.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(199,675)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("675.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.2
Root			$2.17840 - 0.583700i$ of defining polynomial
Character	$\chi$	$=$	675.424
Dual form			675.2.k.b.199.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80664 - 1.04307i) q^{2} +(1.17597 + 2.03684i) q^{4} +(-3.53869 - 2.04307i) q^{7} -0.734191i q^{8} +O(q^{10})$	\(q+(-1.80664 - 1.04307i) q^{2} +(1.17597 + 2.03684i) q^{4} +(-3.53869 - 2.04307i) q^{7} -0.734191i q^{8} +(-0.675970 + 1.17081i) q^{11} +(-0.561237 + 0.324030i) q^{13} +(4.26210 + 7.38217i) q^{14} +(1.58613 - 2.74726i) q^{16} +1.35194i q^{17} -0.648061 q^{19} +(2.44247 - 1.41016i) q^{22} +(4.14827 - 2.39500i) q^{23} +1.35194 q^{26} -9.61033i q^{28} +(-1.93807 + 3.35683i) q^{29} +(3.84823 + 6.66533i) q^{31} +(-7.00279 + 4.04307i) q^{32} +(1.41016 - 2.44247i) q^{34} +7.52420i q^{37} +(1.17081 + 0.675970i) q^{38} +(-0.0898394 - 0.155606i) q^{41} +(-0.710419 - 0.410161i) q^{43} -3.17968 q^{44} -9.99258 q^{46} +(9.44526 + 5.45323i) q^{47} +(4.84823 + 8.39738i) q^{49} +(-1.32000 - 0.762100i) q^{52} +4.17226i q^{53} +(-1.50000 + 2.59808i) q^{56} +(7.00279 - 4.04307i) q^{58} +(-2.08613 - 3.61328i) q^{59} +(1.91016 - 3.30850i) q^{61} -16.0558i q^{62} +10.5242 q^{64} +(7.05113 - 4.07097i) q^{67} +(-2.75368 + 1.58984i) q^{68} +6.11644 q^{71} +12.3445i q^{73} +(7.84823 - 13.5935i) q^{74} +(-0.762100 - 1.32000i) q^{76} +(4.78410 - 2.76210i) q^{77} +(5.17226 - 8.95862i) q^{79} +0.374833i q^{82} +(10.6161 + 6.12920i) q^{83} +(0.855648 + 1.48203i) q^{86} +(0.859601 + 0.496291i) q^{88} -3.00000 q^{89} +2.64806 q^{91} +(9.75648 + 5.63290i) q^{92} +(-11.3761 - 19.7041i) q^{94} +(11.7606 + 6.79001i) q^{97} -20.2281i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4}+O(q^{10}) $ 12 * q + 10 * q^4	$ 12 q + 10 q^{4} - 4 q^{11} + 18 q^{14} - 10 q^{16} - 16 q^{19} + 8 q^{26} + 14 q^{29} - 16 q^{31} - 8 q^{34} - 26 q^{41} - 88 q^{44} - 12 q^{46} - 4 q^{49} - 18 q^{56} + 4 q^{59} - 2 q^{61} + 60 q^{64} + 40 q^{71} + 32 q^{74} + 24 q^{76} + 4 q^{79} + 56 q^{86} - 36 q^{89} + 40 q^{91} - 62 q^{94}+O(q^{100}) $ 12 * q + 10 * q^4 - 4 * q^11 + 18 * q^14 - 10 * q^16 - 16 * q^19 + 8 * q^26 + 14 * q^29 - 16 * q^31 - 8 * q^34 - 26 * q^41 - 88 * q^44 - 12 * q^46 - 4 * q^49 - 18 * q^56 + 4 * q^59 - 2 * q^61 + 60 * q^64 + 40 * q^71 + 32 * q^74 + 24 * q^76 + 4 * q^79 + 56 * q^86 - 36 * q^89 + 40 * q^91 - 62 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.80664	−	1.04307i	−1.27749	−	0.737558i	−0.301103	−	0.953592i	$-0.597355\pi$
$2$	−1.80664	−	1.04307i	−1.27749	−	0.737558i	−0.976386	+	0.216033i	$0.930688\pi$
$3$		0			0
$3$		0			0
$4$	1.17597	+	2.03684i	0.587985	+	1.01842i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.53869	−	2.04307i	−1.33750	−	0.772206i	−0.351064	−	0.936351i	$-0.614180\pi$
$7$	−3.53869	−	2.04307i	−1.33750	−	0.772206i	−0.986436	+	0.164145i	$0.947513\pi$
$8$		−	0.734191i		−	0.259576i
$9$		0			0
$10$		0			0
$11$	−0.675970	+	1.17081i	−0.203813	+	0.353014i	−0.949754	−	0.312998i	$-0.898667\pi$
$11$	−0.675970	+	1.17081i	−0.203813	+	0.353014i	0.745941	+	0.666012i	$0.232000\pi$
$12$		0			0
$13$	−0.561237	+	0.324030i	−0.155659	+	0.0898699i	−0.575806	−	0.817586i	$-0.695312\pi$
$13$	−0.561237	+	0.324030i	−0.155659	+	0.0898699i	0.420147	+	0.907456i	$0.361978\pi$
$14$	4.26210	+	7.38217i	1.13909	+	1.97297i
$15$		0			0
$16$	1.58613	−	2.74726i	0.396533	−	0.686815i
$17$			1.35194i			0.327893i	0.986469	+	0.163947i	$0.0524225\pi$
$17$			1.35194i			0.327893i	−0.986469	+	0.163947i	$0.947577\pi$
$18$		0			0
$19$	−0.648061			−0.148675			−0.0743377	−	0.997233i	$-0.523684\pi$
$19$	−0.648061			−0.148675			−0.0743377	+	0.997233i	$0.523684\pi$
$20$		0			0
$21$		0			0
$22$	2.44247	−	1.41016i	0.520736	−	0.300647i
$23$	4.14827	−	2.39500i	0.864974	−	0.499393i	−0.000700856	−	1.00000i	$-0.500223\pi$
$23$	4.14827	−	2.39500i	0.864974	−	0.499393i	0.865675	+	0.500607i	$0.166890\pi$
$24$		0			0
$25$		0			0
$26$	1.35194			0.265137
$27$		0			0
$28$		−	9.61033i		−	1.81618i
$29$	−1.93807	+	3.35683i	−0.359890	+	0.623349i	−0.987942	−	0.154823i	$-0.950519\pi$
$29$	−1.93807	+	3.35683i	−0.359890	+	0.623349i	0.628052	+	0.778172i	$0.283853\pi$
$30$		0			0
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	0.971457	+	0.237215i	$0.0762345\pi$
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	−0.280295	+	0.959914i	$0.590432\pi$
$32$	−7.00279	+	4.04307i	−1.23793	+	0.714720i
$33$		0			0
$34$	1.41016	−	2.44247i	0.241841	−	0.418880i
$35$		0			0
$36$		0			0
$37$			7.52420i			1.23697i	0.785796	+	0.618485i	$0.212253\pi$
$37$			7.52420i			1.23697i	−0.785796	+	0.618485i	$0.787747\pi$
$38$	1.17081	+	0.675970i	0.189931	+	0.109657i
$39$		0			0
$40$		0			0
$41$	−0.0898394	−	0.155606i	−0.0140306	−	0.0243016i	0.858925	−	0.512102i	$-0.171133\pi$
$41$	−0.0898394	−	0.155606i	−0.0140306	−	0.0243016i	−0.872955	+	0.487800i	$0.837800\pi$
$42$		0			0
$43$	−0.710419	−	0.410161i	−0.108338	−	0.0625489i	0.444852	−	0.895604i	$-0.353256\pi$
$43$	−0.710419	−	0.410161i	−0.108338	−	0.0625489i	−0.553190	+	0.833055i	$0.686590\pi$
$44$	−3.17968			−0.479355
$45$		0			0
$46$	−9.99258			−1.47333
$47$	9.44526	+	5.45323i	1.37773	+	0.795435i	0.991886	−	0.127128i	$-0.0405759\pi$
$47$	9.44526	+	5.45323i	1.37773	+	0.795435i	0.385847	+	0.922563i	$0.373909\pi$
$48$		0			0
$49$	4.84823	+	8.39738i	0.692604	+	1.19963i
$50$		0			0
$51$		0			0
$52$	−1.32000	−	0.762100i	−0.183050	−	0.105684i
$53$			4.17226i			0.573104i	0.958065	+	0.286552i	$0.0925091\pi$
$53$			4.17226i			0.573104i	−0.958065	+	0.286552i	$0.907491\pi$
$54$		0			0
$55$		0			0
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$		0			0
$58$	7.00279	−	4.04307i	0.919512	−	0.530880i
$59$	−2.08613	−	3.61328i	−0.271591	−	0.470409i	0.697678	−	0.716411i	$-0.254216\pi$
$59$	−2.08613	−	3.61328i	−0.271591	−	0.470409i	−0.969269	+	0.246002i	$0.920883\pi$
$60$		0			0
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	−0.717440	−	0.696620i	$-0.754686\pi$
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	0.962011	+	0.273011i	$0.0880195\pi$
$62$		−	16.0558i		−	2.03909i
$63$		0			0
$64$	10.5242			1.31552
$65$		0			0
$66$		0			0
$67$	7.05113	−	4.07097i	0.861433	−	0.497349i	−0.00305885	−	0.999995i	$-0.500974\pi$
$67$	7.05113	−	4.07097i	0.861433	−	0.497349i	0.864492	+	0.502647i	$0.167640\pi$
$68$	−2.75368	+	1.58984i	−0.333933	+	0.192796i
$69$		0			0
$70$		0			0
$71$	6.11644			0.725888			0.362944	−	0.931811i	$-0.381772\pi$
$71$	6.11644			0.725888			0.362944	+	0.931811i	$0.381772\pi$
$72$		0			0
$73$			12.3445i			1.44482i	0.691467	+	0.722408i	$0.256965\pi$
$73$			12.3445i			1.44482i	−0.691467	+	0.722408i	$0.743035\pi$
$74$	7.84823	−	13.5935i	0.912338	−	1.58022i
$75$		0			0
$76$	−0.762100	−	1.32000i	−0.0874188	−	0.151414i
$77$	4.78410	−	2.76210i	0.545198	−	0.314770i
$78$		0			0
$79$	5.17226	−	8.95862i	0.581925	−	1.00792i	−0.413326	−	0.910583i	$-0.635633\pi$
$79$	5.17226	−	8.95862i	0.581925	−	1.00792i	0.995251	−	0.0973403i	$-0.0310335\pi$
$80$		0			0
$81$		0			0
$82$			0.374833i			0.0413934i
$83$	10.6161	+	6.12920i	1.16527	+	0.672767i	0.952560	−	0.304350i	$-0.0984392\pi$
$83$	10.6161	+	6.12920i	1.16527	+	0.672767i	0.212706	+	0.977116i	$0.431772\pi$
$84$		0			0
$85$		0			0
$86$	0.855648	+	1.48203i	0.0922669	+	0.159811i
$87$		0			0
$88$	0.859601	+	0.496291i	0.0916338	+	0.0529048i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	2.64806			0.277592
$92$	9.75648	+	5.63290i	1.01718	+	0.587271i
$93$		0			0
$94$	−11.3761	−	19.7041i	−1.17336	−	2.03232i
$95$		0			0
$96$		0			0
$97$	11.7606	+	6.79001i	1.19411	+	0.689421i	0.959237	−	0.282605i	$-0.0911984\pi$
$97$	11.7606	+	6.79001i	1.19411	+	0.689421i	0.234876	+	0.972025i	$0.424532\pi$
$98$		−	20.2281i		−	2.04334i
$99$		0			0
$100$		0			0
$101$	−0.734191	+	1.27166i	−0.0730547	+	0.126535i	−0.900239	−	0.435397i	$-0.856608\pi$
$101$	−0.734191	+	1.27166i	−0.0730547	+	0.126535i	0.827184	+	0.561931i	$0.189941\pi$
$102$		0			0
$103$	−6.51615	+	3.76210i	−0.642055	+	0.370691i	−0.785406	−	0.618981i	$-0.787546\pi$
$103$	−6.51615	+	3.76210i	−0.642055	+	0.370691i	0.143351	+	0.989672i	$0.454212\pi$
$104$	0.237900	+	0.412055i	0.0233280	+	0.0404053i
$105$		0			0
$106$	4.35194	−	7.53778i	0.422698	−	0.732134i
$107$		−	1.20999i		−	0.116974i	−0.998288	−	0.0584871i	$-0.981372\pi$
$107$		−	1.20999i		−	0.116974i	0.998288	−	0.0584871i	$-0.0186277\pi$
$108$		0			0
$109$	−14.1042			−1.35094			−0.675469	−	0.737388i	$-0.736059\pi$
$109$	−14.1042			−1.35094			−0.675469	+	0.737388i	$0.736059\pi$
$110$		0			0
$111$		0			0
$112$	−11.2257	+	6.48113i	−1.06072	+	0.612410i
$113$	−10.3270	+	5.96227i	−0.971478	+	0.560883i	−0.899687	−	0.436537i	$-0.856205\pi$
$113$	−10.3270	+	5.96227i	−0.971478	+	0.560883i	−0.0717915	+	0.997420i	$0.522872\pi$
$114$		0			0
$115$		0			0
$116$	−9.11644			−0.846440
$117$		0			0
$118$			8.70388i			0.801257i
$119$	2.76210	−	4.78410i	0.253201	−	0.438557i
$120$		0			0
$121$	4.58613	+	7.94341i	0.416921	+	0.722128i
$122$	−6.90195	+	3.98484i	−0.624873	+	0.360771i
$123$		0			0
$124$	−9.05080	+	15.6765i	−0.812786	+	1.40779i
$125$		0			0
$126$		0			0
$127$		−	7.07871i		−	0.628134i	−0.949401	−	0.314067i	$-0.898308\pi$
$127$		−	7.07871i		−	0.628134i	0.949401	−	0.314067i	$-0.101692\pi$
$128$	−5.00787	−	2.89130i	−0.442637	−	0.255557i
$129$		0			0
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	2.29329	+	1.32403i	0.198853	+	0.114808i
$134$	−16.9852			−1.46729
$135$		0			0
$136$	0.992582			0.0851132
$137$	−6.46781	−	3.73419i	−0.552582	−	0.319033i	0.197581	−	0.980287i	$-0.436692\pi$
$137$	−6.46781	−	3.73419i	−0.552582	−	0.319033i	−0.750163	+	0.661253i	$0.770025\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$		0			0
$142$	−11.0502	−	6.37985i	−0.927314	−	0.535385i
$143$		−	0.876139i		−	0.0732664i
$144$		0			0
$145$		0			0
$146$	12.8761	−	22.3021i	1.06564	−	1.84574i
$147$		0			0
$148$	−15.3256	+	8.84823i	−1.25976	+	0.727320i
$149$	5.29241	+	9.16673i	0.433571	+	0.750968i	0.997178	−	0.0750759i	$-0.0239199\pi$
$149$	5.29241	+	9.16673i	0.433571	+	0.750968i	−0.563607	+	0.826043i	$0.690587\pi$
$150$		0			0
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	0.240917	+	0.970546i	$0.422552\pi$
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	−0.960976	+	0.276633i	$0.910781\pi$
$152$			0.475800i			0.0385925i
$153$		0			0
$154$	−11.5242			−0.928646
$155$		0			0
$156$		0			0
$157$	−2.19245	+	1.26581i	−0.174976	+	0.101023i	−0.584930	−	0.811084i	$-0.698878\pi$
$157$	−2.19245	+	1.26581i	−0.174976	+	0.101023i	0.409954	+	0.912106i	$0.365545\pi$
$158$	−18.6888	+	10.7900i	−1.48680	+	0.858407i
$159$		0			0
$160$		0			0
$161$	−19.5726			−1.54254
$162$		0			0
$163$		−	8.47580i		−	0.663876i	−0.943301	−	0.331938i	$-0.892298\pi$
$163$		−	8.47580i		−	0.663876i	0.943301	−	0.331938i	$-0.107702\pi$
$164$	0.211297	−	0.365977i	0.0164995	−	0.0285780i
$165$		0			0
$166$	−12.7863	−	22.1465i	−0.992409	−	1.71890i
$167$	−11.0281	+	6.36710i	−0.853383	+	0.492701i	−0.861791	−	0.507264i	$-0.830657\pi$
$167$	−11.0281	+	6.36710i	−0.853383	+	0.492701i	0.00840816	+	0.999965i	$0.497324\pi$
$168$		0			0
$169$	−6.29001	+	10.8946i	−0.483847	+	0.838047i
$170$		0			0
$171$		0			0
$172$		−	1.92935i		−	0.147111i
$173$	−19.9605	−	11.5242i	−1.51757	−	0.876169i	−0.999787	−	0.0206561i	$-0.993424\pi$
$173$	−19.9605	−	11.5242i	−1.51757	−	0.876169i	−0.517782	−	0.855513i	$-0.673242\pi$
$174$		0			0
$175$		0			0
$176$	2.14435	+	3.71413i	0.161637	+	0.279963i
$177$		0			0
$178$	5.41993	+	3.12920i	0.406241	+	0.234543i
$179$	2.22808			0.166534			0.0832672	−	0.996527i	$-0.473465\pi$
$179$	2.22808			0.166534			0.0832672	+	0.996527i	$0.473465\pi$
$180$		0			0
$181$	0.468382			0.0348146			0.0174073	−	0.999848i	$-0.494459\pi$
$181$	0.468382			0.0348146			0.0174073	+	0.999848i	$0.494459\pi$
$182$	−4.78410	−	2.76210i	−0.354621	−	0.204740i
$183$		0			0
$184$	−1.75839	−	3.04562i	−0.129630	−	0.224526i
$185$		0			0
$186$		0			0
$187$	−1.58287	−	0.913870i	−0.115751	−	0.0668288i
$188$			25.6513i			1.87081i
$189$		0			0
$190$		0			0
$191$	−10.1140	+	17.5180i	−0.731826	+	1.26756i	0.224276	+	0.974526i	$0.427998\pi$
$191$	−10.1140	+	17.5180i	−0.731826	+	1.26756i	−0.956102	+	0.293034i	$0.905335\pi$
$192$		0			0
$193$	17.2593	−	9.96467i	1.24235	−	0.717273i	0.272780	−	0.962076i	$-0.412057\pi$
$193$	17.2593	−	9.96467i	1.24235	−	0.717273i	0.969573	+	0.244804i	$0.0787235\pi$
$194$	−14.1648	−	24.5342i	−1.01698	−	1.76145i
$195$		0			0
$196$	−11.4027	+	19.7501i	−0.814482	+	1.41072i
$197$			15.5800i			1.11003i	0.831840	+	0.555015i	$0.187288\pi$
$197$			15.5800i			1.11003i	−0.831840	+	0.555015i	$0.812712\pi$
$198$		0			0
$199$	−3.58482			−0.254121			−0.127061	−	0.991895i	$-0.540554\pi$
$199$	−3.58482			−0.254121			−0.127061	+	0.991895i	$0.540554\pi$
$200$		0			0
$201$		0			0
$202$	2.65284	−	1.53162i	0.186653	−	0.107764i
$203$	13.7165	−	7.91920i	0.962707	−	0.555819i
$204$		0			0
$205$		0			0
$206$	15.6965			1.09362
$207$		0			0
$208$			2.05582i			0.142545i
$209$	0.438069	−	0.758758i	0.0303019	−	0.0524844i
$210$		0			0
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	−0.999826	−	0.0186518i	$-0.994063\pi$
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	0.483760	−	0.875201i	$-0.339271\pi$
$212$	−8.49822	+	4.90645i	−0.583660	+	0.336976i
$213$		0			0
$214$	−1.26210	+	2.18602i	−0.0862754	+	0.149433i
$215$		0			0
$216$		0			0
$217$		−	31.4487i		−	2.13488i
$218$	25.4813	+	14.7116i	1.72581	+	0.996396i
$219$		0			0
$220$		0			0
$221$	−0.438069	−	0.758758i	−0.0294677	−	0.0510396i
$222$		0			0
$223$	−23.2363	−	13.4155i	−1.55602	−	0.898368i	−0.997631	−	0.0687878i	$-0.978087\pi$
$223$	−23.2363	−	13.4155i	−1.55602	−	0.898368i	−0.558388	−	0.829580i	$-0.688580\pi$
$224$	33.0410			2.20764
$225$		0			0
$226$	24.8761			1.65474
$227$	1.17081	+	0.675970i	0.0777096	+	0.0448657i	0.538351	−	0.842721i	$-0.319047\pi$
$227$	1.17081	+	0.675970i	0.0777096	+	0.0448657i	−0.460642	+	0.887586i	$0.652381\pi$
$228$		0			0
$229$	−4.11775	−	7.13215i	−0.272108	−	0.471306i	0.697293	−	0.716786i	$-0.254388\pi$
$229$	−4.11775	−	7.13215i	−0.272108	−	0.471306i	−0.969402	+	0.245480i	$0.921054\pi$
$230$		0			0
$231$		0			0
$232$	2.46456	+	1.42291i	0.161806	+	0.0934188i
$233$			8.58744i			0.562582i	0.959623	+	0.281291i	$0.0907626\pi$
$233$			8.58744i			0.562582i	−0.959623	+	0.281291i	$0.909237\pi$
$234$		0			0
$235$		0			0
$236$	4.90645	−	8.49822i	0.319383	−	0.553187i
$237$		0			0
$238$	−9.98025	+	5.76210i	−0.646923	+	0.373501i
$239$	11.9623	+	20.7193i	0.773775	+	1.34022i	0.935480	+	0.353378i	$0.114967\pi$
$239$	11.9623	+	20.7193i	0.773775	+	1.34022i	−0.161706	+	0.986839i	$0.551700\pi$
$240$		0			0
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	−0.747860	−	0.663857i	$-0.768919\pi$
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	0.948847	+	0.315737i	$0.102252\pi$
$242$		−	19.1345i		−	1.23001i
$243$		0			0
$244$	8.98516			0.575216
$245$		0			0
$246$		0			0
$247$	0.363716	−	0.209991i	0.0231427	−	0.0133614i
$248$	4.89363	−	2.82534i	0.310746	−	0.179409i
$249$		0			0
$250$		0			0
$251$	28.5726			1.80349			0.901743	−	0.432272i	$-0.142288\pi$
$251$	28.5726			1.80349			0.901743	+	0.432272i	$0.142288\pi$
$252$		0			0
$253$			6.47580i			0.407130i
$254$	−7.38356	+	12.7887i	−0.463286	+	0.802434i
$255$		0			0
$256$	−4.49258	−	7.78138i	−0.280786	−	0.486336i
$257$	15.5885	−	9.00000i	0.972381	−	0.561405i	0.0724199	−	0.997374i	$-0.476928\pi$
$257$	15.5885	−	9.00000i	0.972381	−	0.561405i	0.899961	+	0.435970i	$0.143595\pi$
$258$		0			0
$259$	15.3724	−	26.6258i	0.955196	−	1.65445i
$260$		0			0
$261$		0			0
$262$			12.5168i			0.773289i
$263$	−27.5991	−	15.9344i	−1.70183	−	0.982555i	−0.943904	−	0.330220i	$-0.892877\pi$
$263$	−27.5991	−	15.9344i	−1.70183	−	0.982555i	−0.757931	−	0.652335i	$-0.773789\pi$
$264$		0			0
$265$		0			0
$266$	−2.76210	−	4.78410i	−0.169355	−	0.293332i
$267$		0			0
$268$	16.5838	+	9.57468i	1.01302	+	0.584867i
$269$	−31.4971			−1.92041			−0.960207	−	0.279289i	$-0.909901\pi$
$269$	−31.4971			−1.92041			−0.960207	+	0.279289i	$0.909901\pi$
$270$		0			0
$271$	−3.24030			−0.196834			−0.0984172	−	0.995145i	$-0.531378\pi$
$271$	−3.24030			−0.196834			−0.0984172	+	0.995145i	$0.531378\pi$
$272$	3.71413	+	2.14435i	0.225202	+	0.130020i
$273$		0			0
$274$	7.79001	+	13.4927i	0.470612	+	0.815123i
$275$		0			0
$276$		0			0
$277$	4.83660	+	2.79241i	0.290603	+	0.167780i	0.638214	−	0.769859i	$-0.279674\pi$
$277$	4.83660	+	2.79241i	0.290603	+	0.167780i	−0.347611	+	0.937639i	$0.613007\pi$
$278$		−	16.6890i		−	1.00094i
$279$		0			0
$280$		0			0
$281$	−12.0521	+	20.8749i	−0.718969	+	1.24529i	0.242440	+	0.970166i	$0.422052\pi$
$281$	−12.0521	+	20.8749i	−0.718969	+	1.24529i	−0.961409	+	0.275124i	$0.911281\pi$
$282$		0			0
$283$	9.12989	−	5.27114i	0.542715	−	0.313337i	−0.203463	−	0.979083i	$-0.565220\pi$
$283$	9.12989	−	5.27114i	0.542715	−	0.313337i	0.746179	+	0.665746i	$0.231886\pi$
$284$	7.19275	+	12.4582i	0.426811	+	0.739259i
$285$		0			0
$286$	−0.913870	+	1.58287i	−0.0540383	+	0.0935970i
$287$			0.734191i			0.0433379i
$288$		0			0
$289$	15.1723			0.892486
$290$		0			0
$291$		0			0
$292$	−25.1438	+	14.5168i	−1.47143	+	0.849530i
$293$	16.4481	−	9.49629i	0.960906	−	0.554779i	0.0644541	−	0.997921i	$-0.479469\pi$
$293$	16.4481	−	9.49629i	0.960906	−	0.554779i	0.896452	+	0.443141i	$0.146136\pi$
$294$		0			0
$295$		0			0
$296$	5.52420			0.321088
$297$		0			0
$298$		−	22.0813i		−	1.27914i
$299$	−1.55211	+	2.68833i	−0.0897607	+	0.155470i
$300$		0			0
$301$	1.67597	+	2.90286i	0.0966013	+	0.167318i
$302$	31.9712	−	18.4586i	1.83973	−	1.06217i
$303$		0			0
$304$	−1.02791	+	1.78039i	−0.0589546	+	0.102112i
$305$		0			0
$306$		0			0
$307$			29.4791i			1.68246i	0.540679	+	0.841229i	$0.318167\pi$
$307$			29.4791i			1.68246i	−0.540679	+	0.841229i	$0.681833\pi$
$308$	11.2519	+	6.49629i	0.641137	+	0.370161i
$309$		0			0
$310$		0			0
$311$	−4.70628	−	8.15152i	−0.266869	−	0.462230i	0.701183	−	0.712982i	$-0.252656\pi$
$311$	−4.70628	−	8.15152i	−0.266869	−	0.462230i	−0.968052	+	0.250751i	$0.919322\pi$
$312$		0			0
$313$	10.0641	+	5.81050i	0.568855	+	0.328429i	0.756692	−	0.653771i	$-0.226814\pi$
$313$	10.0641	+	5.81050i	0.568855	+	0.328429i	−0.187837	+	0.982200i	$0.560148\pi$
$314$	5.28128			0.298040
$315$		0			0
$316$	24.3297			1.36865
$317$	−7.94984	−	4.58984i	−0.446507	−	0.257791i	0.259847	−	0.965650i	$-0.416328\pi$
$317$	−7.94984	−	4.58984i	−0.446507	−	0.257791i	−0.706354	+	0.707859i	$0.749661\pi$
$318$		0			0
$319$	−2.62015	−	4.53824i	−0.146700	−	0.254092i
$320$		0			0
$321$		0			0
$322$	35.3607	+	20.4155i	1.97057	+	1.13771i
$323$		−	0.876139i		−	0.0487497i
$324$		0			0
$325$		0			0
$326$	−8.84081	+	15.3127i	−0.489647	+	0.848094i
$327$		0			0
$328$	−0.114245	+	0.0659593i	−0.00630812	+	0.00364199i
$329$	−22.2826	−	38.5946i	−1.22848	−	2.12779i
$330$		0			0
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	−0.749582	−	0.661912i	$-0.769745\pi$
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	0.948023	+	0.318201i	$0.103079\pi$
$332$			28.8310i			1.58231i
$333$		0			0
$334$	26.5652			1.45358
$335$		0			0
$336$		0			0
$337$	1.97791	−	1.14195i	0.107744	−	0.0622059i	−0.445160	−	0.895451i	$-0.646853\pi$
$337$	1.97791	−	1.14195i	0.107744	−	0.0622059i	0.552904	+	0.833245i	$0.313520\pi$
$338$	22.7276	−	13.1218i	1.23622	−	0.713731i
$339$		0			0
$340$		0			0
$341$	−10.4051			−0.563470
$342$		0			0
$343$		−	11.0181i		−	0.594921i
$344$	−0.301136	+	0.521583i	−0.0162362	+	0.0281219i
$345$		0			0
$346$	24.0410	+	41.6402i	1.29245	+	2.23859i
$347$	0.613740	−	0.354343i	0.0329473	−	0.0190221i	−0.483436	−	0.875380i	$-0.660611\pi$
$347$	0.613740	−	0.354343i	0.0329473	−	0.0190221i	0.516383	+	0.856358i	$0.327278\pi$
$348$		0			0
$349$	−10.6723	+	18.4849i	−0.571273	+	0.989474i	0.425163	+	0.905117i	$0.360217\pi$
$349$	−10.6723	+	18.4849i	−0.571273	+	0.989474i	−0.996436	+	0.0843569i	$0.973116\pi$
$350$		0			0
$351$		0			0
$352$		−	10.9320i		−	0.582675i
$353$	8.74408	+	5.04840i	0.465401	+	0.268699i	0.714312	−	0.699827i	$-0.246740\pi$
$353$	8.74408	+	5.04840i	0.465401	+	0.268699i	−0.248912	+	0.968526i	$0.580073\pi$
$354$		0			0
$355$		0			0
$356$	−3.52791	−	6.11052i	−0.186979	−	0.323857i
$357$		0			0
$358$	−4.02534	−	2.32403i	−0.212746	−	0.122829i
$359$	30.5578			1.61278			0.806388	−	0.591386i	$-0.201419\pi$
$359$	30.5578			1.61278			0.806388	+	0.591386i	$0.201419\pi$
$360$		0			0
$361$	−18.5800			−0.977896
$362$	−0.846198	−	0.488553i	−0.0444752	−	0.0256778i
$363$		0			0
$364$	3.11404	+	5.39367i	0.163220	+	0.282705i
$365$		0			0
$366$		0			0
$367$	6.21778	+	3.58984i	0.324566	+	0.187388i	0.653426	−	0.756991i	$-0.273331\pi$
$367$	6.21778	+	3.58984i	0.324566	+	0.187388i	−0.328860	+	0.944379i	$0.606664\pi$
$368$		−	15.1952i		−	0.792102i
$369$		0			0
$370$		0			0
$371$	8.52420	−	14.7643i	0.442554	−	0.766527i
$372$		0			0
$373$	18.9872	−	10.9623i	0.983120	−	0.567605i	0.0799096	−	0.996802i	$-0.474537\pi$
$373$	18.9872	−	10.9623i	0.983120	−	0.567605i	0.903211	+	0.429197i	$0.141204\pi$
$374$	1.90645	+	3.30207i	0.0985803	+	0.170746i
$375$		0			0
$376$	4.00371	−	6.93463i	0.206476	−	0.357626i
$377$		−	2.51197i		−	0.129373i
$378$		0			0
$379$	17.3929			0.893414			0.446707	−	0.894680i	$-0.352597\pi$
$379$	17.3929			0.893414			0.446707	+	0.894680i	$0.352597\pi$
$380$		0			0
$381$		0			0
$382$	36.5449	−	21.0992i	1.86980	−	1.07953i
$383$	0.412055	−	0.237900i	0.0210550	−	0.0121561i	−0.489436	−	0.872039i	$-0.662797\pi$
$383$	0.412055	−	0.237900i	0.0210550	−	0.0121561i	0.510491	+	0.859883i	$0.329464\pi$
$384$		0			0
$385$		0			0
$386$	−41.5752			−2.11612
$387$		0			0
$388$			31.9394i			1.62148i
$389$	2.79372	−	4.83886i	0.141647	−	0.245340i	−0.786470	−	0.617629i	$-0.788094\pi$
$389$	2.79372	−	4.83886i	0.141647	−	0.245340i	0.928117	+	0.372289i	$0.121427\pi$
$390$		0			0
$391$	3.23790	+	5.60821i	0.163748	+	0.283619i
$392$	6.16528	−	3.55953i	0.311394	−	0.179783i
$393$		0			0
$394$	16.2510	−	28.1475i	0.818712	−	1.41805i
$395$		0			0
$396$		0			0
$397$			3.75228i			0.188321i	0.995557	+	0.0941607i	$0.0300168\pi$
$397$			3.75228i			0.188321i	−0.995557	+	0.0941607i	$0.969983\pi$
$398$	6.47649	+	3.73921i	0.324637	+	0.187429i
$399$		0			0
$400$		0			0
$401$	11.7826	+	20.4080i	0.588394	+	1.01913i	0.994443	+	0.105278i	$0.0335731\pi$
$401$	11.7826	+	20.4080i	0.588394	+	1.01913i	−0.406048	+	0.913852i	$0.633094\pi$
$402$		0			0
$403$	−4.31954	−	2.49389i	−0.215172	−	0.124229i
$404$	−3.45355			−0.171820
$405$		0			0
$406$	−33.0410			−1.63980
$407$	−8.80944	−	5.08613i	−0.436668	−	0.252110i
$408$		0			0
$409$	0.524200	+	0.907940i	0.0259200	+	0.0448948i	0.878694	−	0.477385i	$-0.158415\pi$
$409$	0.524200	+	0.907940i	0.0259200	+	0.0448948i	−0.852774	+	0.522279i	$0.825082\pi$
$410$		0			0
$411$		0			0
$412$	−15.3256	−	8.84823i	−0.755037	−	0.435921i
$413$			17.0484i			0.838897i
$414$		0			0
$415$		0			0
$416$	2.62015	−	4.53824i	0.128464	−	0.222505i
$417$		0			0
$418$	−1.58287	+	0.913870i	−0.0774207	+	0.0446988i
$419$	12.9599	+	22.4471i	0.633131	+	1.09661i	0.986908	+	0.161285i	$0.0515638\pi$
$419$	12.9599	+	22.4471i	0.633131	+	1.09661i	−0.353777	+	0.935330i	$0.615103\pi$
$420$		0			0
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	−0.943977	−	0.330011i	$-0.892948\pi$
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	0.757786	+	0.652503i	$0.226281\pi$
$422$			31.2765i			1.52252i
$423$		0			0
$424$	3.06324			0.148764
$425$		0			0
$426$		0			0
$427$	−13.5189	+	7.80516i	−0.654227	+	0.377718i
$428$	2.46456	−	1.42291i	0.119129	−	0.0687791i
$429$		0			0
$430$		0			0
$431$	−7.98516			−0.384632			−0.192316	−	0.981333i	$-0.561600\pi$
$431$	−7.98516			−0.384632			−0.192316	+	0.981333i	$0.561600\pi$
$432$		0			0
$433$			12.5120i			0.601287i	0.953737	+	0.300644i	$0.0972014\pi$
$433$			12.5120i			0.601287i	−0.953737	+	0.300644i	$0.902799\pi$
$434$	−32.8031	+	56.8166i	−1.57460	+	2.72728i
$435$		0			0
$436$	−16.5861	−	28.7280i	−0.794332	−	1.37582i
$437$	−2.68833	+	1.55211i	−0.128600	+	0.0742474i
$438$		0			0
$439$	−4.38225	+	7.59028i	−0.209153	+	0.362264i	−0.951448	−	0.307809i	$-0.900404\pi$
$439$	−4.38225	+	7.59028i	−0.209153	+	0.362264i	0.742295	+	0.670074i	$0.233737\pi$
$440$		0			0
$441$		0			0
$442$			1.82774i			0.0869367i
$443$	−3.17914	−	1.83548i	−0.151046	−	0.0872062i	0.422572	−	0.906329i	$-0.361127\pi$
$443$	−3.17914	−	1.83548i	−0.151046	−	0.0872062i	−0.573618	+	0.819123i	$0.694461\pi$
$444$		0			0
$445$		0			0
$446$	27.9865	+	48.4740i	1.32520	+	2.29531i
$447$		0			0
$448$	−37.2419	−	21.5016i	−1.75951	−	1.01586i
$449$	28.1723			1.32953			0.664766	−	0.747052i	$-0.268531\pi$
$449$	28.1723			1.32953			0.664766	+	0.747052i	$0.268531\pi$
$450$		0			0
$451$	0.242915			0.0114384
$452$	−24.2884	−	14.0229i	−1.14243	−	0.659581i
$453$		0			0
$454$	−1.41016	−	2.44247i	−0.0661821	−	0.114631i
$455$		0			0
$456$		0			0
$457$	−30.5375	−	17.6308i	−1.42848	−	0.824735i	−0.431482	−	0.902122i	$-0.642009\pi$
$457$	−30.5375	−	17.6308i	−1.42848	−	0.824735i	−0.997001	+	0.0773867i	$0.975342\pi$
$458$			17.1803i			0.802784i
$459$		0			0
$460$		0			0
$461$	17.3384	−	30.0310i	0.807530	−	1.39868i	−0.107039	−	0.994255i	$-0.534137\pi$
$461$	17.3384	−	30.0310i	0.807530	−	1.39868i	0.914570	−	0.404428i	$-0.132530\pi$
$462$		0			0
$463$	−6.45080	+	3.72437i	−0.299794	+	0.173086i	−0.642350	−	0.766411i	$-0.722041\pi$
$463$	−6.45080	+	3.72437i	−0.299794	+	0.173086i	0.342556	+	0.939497i	$0.388707\pi$
$464$	6.14806	+	10.6488i	0.285417	+	0.494356i
$465$		0			0
$466$	8.95725	−	15.5144i	0.414937	−	0.718692i
$467$		−	29.9655i		−	1.38664i	−0.720630	−	0.693319i	$-0.756148\pi$
$467$		−	29.9655i		−	1.38664i	0.720630	−	0.693319i	$-0.243852\pi$
$468$		0			0
$469$	−33.2691			−1.53622
$470$		0			0
$471$		0			0
$472$	−2.65284	+	1.53162i	−0.122107	+	0.0704984i
$473$	0.960443	−	0.554512i	0.0441612	−	0.0254965i
$474$		0			0
$475$		0			0
$476$	12.9926			0.595514
$477$		0			0
$478$		−	49.9097i		−	2.28282i
$479$	3.99258	−	6.91535i	0.182426	−	0.315971i	−0.760280	−	0.649595i	$-0.774938\pi$
$479$	3.99258	−	6.91535i	0.182426	−	0.315971i	0.942706	+	0.333625i	$0.108272\pi$
$480$		0			0
$481$	−2.43807	−	4.22286i	−0.111166	−	0.192546i
$482$	−11.2740	+	6.50904i	−0.513516	+	0.296479i
$483$		0			0
$484$	−10.7863	+	18.6824i	−0.490286	+	0.849201i
$485$		0			0
$486$		0			0
$487$		−	11.9442i		−	0.541243i	−0.962686	−	0.270621i	$-0.912771\pi$
$487$		−	11.9442i		−	0.541243i	0.962686	−	0.270621i	$-0.0872291\pi$
$488$	−2.42907	−	1.40242i	−0.109959	−	0.0634847i
$489$		0			0
$490$		0			0
$491$	−4.61033	−	7.98533i	−0.208061	−	0.360373i	0.743042	−	0.669244i	$-0.233382\pi$
$491$	−4.61033	−	7.98533i	−0.208061	−	0.360373i	−0.951104	+	0.308872i	$0.900049\pi$
$492$		0			0
$493$	−4.53824	−	2.62015i	−0.204392	−	0.118006i
$494$	−0.876139			−0.0394193
$495$		0			0
$496$	24.4152			1.09627
$497$	−21.6442	−	12.4963i	−0.970876	−	0.560535i
$498$		0			0
$499$	15.0861	+	26.1299i	0.675348	+	1.16974i	0.976367	+	0.216119i	$0.0693399\pi$
$499$	15.0861	+	26.1299i	0.675348	+	1.16974i	−0.301019	+	0.953618i	$0.597327\pi$
$500$		0			0
$501$		0			0
$502$	−51.6204	−	29.8031i	−2.30393	−	1.33018i
$503$		−	10.5981i		−	0.472546i	−0.971687	−	0.236273i	$-0.924074\pi$
$503$		−	10.5981i		−	0.472546i	0.971687	−	0.236273i	$-0.0759260\pi$
$504$		0			0
$505$		0			0
$506$	6.75468	−	11.6995i	0.300282	−	0.520104i
$507$		0			0
$508$	14.4182	−	8.32435i	0.639704	−	0.369333i
$509$	−14.3761	−	24.9002i	−0.637211	−	1.10368i	−0.986042	−	0.166496i	$-0.946755\pi$
$509$	−14.3761	−	24.9002i	−0.637211	−	1.10368i	0.348831	−	0.937186i	$-0.386579\pi$
$510$		0			0
$511$	25.2207	−	43.6835i	1.11570	−	1.93244i
$512$			30.3094i			1.33950i
$513$		0			0
$514$	−37.5503			−1.65627
$515$		0			0
$516$		0			0
$517$	−12.7694	+	7.37243i	−0.561599	+	0.324239i
$518$	−55.5449	+	32.0689i	−2.44050	+	1.40903i
$519$		0			0
$520$		0			0
$521$	36.0942			1.58132			0.790658	−	0.612259i	$-0.209739\pi$
$521$	36.0942			1.58132			0.790658	+	0.612259i	$0.209739\pi$
$522$		0			0
$523$		−	11.1297i		−	0.486669i	−0.969942	−	0.243334i	$-0.921759\pi$
$523$		−	11.1297i		−	0.486669i	0.969942	−	0.243334i	$-0.0782412\pi$
$524$	7.05582	−	12.2210i	0.308235	−	0.533878i
$525$		0			0
$526$	33.2411	+	57.5754i	1.44938	+	2.51041i
$527$	−9.01112	+	5.20257i	−0.392531	+	0.226628i
$528$		0			0
$529$	−0.0279088	+	0.0483395i	−0.00121343	+	0.00210172i
$530$		0			0
$531$		0			0
$532$			6.22808i			0.270021i
$533$	0.100842	+	0.0582214i	0.00436797	+	0.00252185i
$534$		0			0
$535$		0			0
$536$	−2.98887	−	5.17688i	−0.129100	−	0.223607i
$537$		0			0
$538$	56.9040	+	32.8536i	2.45331	+	1.41642i
$539$	−13.1090			−0.564646
$540$		0			0
$541$	−34.7374			−1.49348			−0.746740	−	0.665116i	$-0.768382\pi$
$541$	−34.7374			−1.49348			−0.746740	+	0.665116i	$0.768382\pi$
$542$	5.85407	+	3.37985i	0.251454	+	0.145177i
$543$		0			0
$544$	−5.46598	−	9.46735i	−0.234352	−	0.405909i
$545$		0			0
$546$		0			0
$547$	2.35087	+	1.35727i	0.100516	+	0.0580328i	0.549415	−	0.835549i	$-0.314851\pi$
$547$	2.35087	+	1.35727i	0.100516	+	0.0580328i	−0.448899	+	0.893582i	$0.648184\pi$
$548$		−	17.5652i		−	0.750347i
$549$		0			0
$550$		0			0
$551$	1.25599	−	2.17543i	0.0535068	−	0.0926766i
$552$		0			0
$553$	−36.6061	+	21.1345i	−1.55665	+	0.898732i
$554$	−5.82534	−	10.0898i	−0.247495	−	0.428674i
$555$		0			0
$556$	−9.40776	+	16.2947i	−0.398978	+	0.691050i
$557$			8.93676i			0.378663i	0.981913	+	0.189331i	$0.0606321\pi$
$557$			8.93676i			0.378663i	−0.981913	+	0.189331i	$0.939368\pi$
$558$		0			0
$559$	0.531618			0.0224850
$560$		0			0
$561$		0			0
$562$	43.5477	−	25.1423i	1.83695	−	1.06056i
$563$	−8.10826	+	4.68130i	−0.341722	+	0.197293i	−0.661033	−	0.750357i	$-0.729882\pi$
$563$	−8.10826	+	4.68130i	−0.341722	+	0.197293i	0.319311	+	0.947650i	$0.396549\pi$
$564$		0			0
$565$		0			0
$566$	−21.9926			−0.924417
$567$		0			0
$568$		−	4.49064i		−	0.188423i
$569$	−17.9368	+	31.0674i	−0.751948	+	1.30241i	0.194929	+	0.980817i	$0.437552\pi$
$569$	−17.9368	+	31.0674i	−0.751948	+	1.30241i	−0.946877	+	0.321595i	$0.895781\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	1.78455	−	1.03031i	0.0746159	−	0.0430795i
$573$		0			0
$574$	0.765809	−	1.32642i	0.0319643	−	0.0553637i
$575$		0			0
$576$		0			0
$577$			1.35675i			0.0564821i	0.999601	+	0.0282411i	$0.00899060\pi$
$577$			1.35675i			0.0564821i	−0.999601	+	0.0282411i	$0.991009\pi$
$578$	−27.4108	−	15.8257i	−1.14014	−	0.658260i
$579$		0			0
$580$		0			0
$581$	−25.0447	−	43.3787i	−1.03903	−	1.79965i
$582$		0			0
$583$	−4.88494	−	2.82032i	−0.202314	−	0.116806i
$584$	9.06324			0.375039
$585$		0			0
$586$	−39.6210			−1.63673
$587$	24.9329	+	14.3950i	1.02909	+	0.594145i	0.916724	−	0.399521i	$-0.130824\pi$
$587$	24.9329	+	14.3950i	1.02909	+	0.594145i	0.112366	+	0.993667i	$0.464157\pi$
$588$		0			0
$589$	−2.49389	−	4.31954i	−0.102759	−	0.177984i
$590$		0			0
$591$		0			0
$592$	20.6709	+	11.9344i	0.849570	+	0.490499i
$593$			30.9171i			1.26961i	0.772671	+	0.634807i	$0.218920\pi$
$593$			30.9171i			1.26961i	−0.772671	+	0.634807i	$0.781080\pi$
$594$		0			0
$595$		0			0
$596$	−12.4474	+	21.5596i	−0.509867	+	0.883115i
$597$		0			0
$598$	5.60821	−	3.23790i	0.229337	−	0.132408i
$599$	−0.696460	−	1.20630i	−0.0284566	−	0.0492882i	0.851446	−	0.524442i	$-0.175726\pi$
$599$	−0.696460	−	1.20630i	−0.0284566	−	0.0492882i	−0.879903	+	0.475153i	$0.842393\pi$
$600$		0			0
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	−0.941878	−	0.335956i	$-0.890941\pi$
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	0.761885	+	0.647712i	$0.224274\pi$
$602$		−	6.99258i		−	0.284996i
$603$		0			0
$604$	−41.6210			−1.69353
$605$		0			0
$606$		0			0
$607$	−1.86783	+	1.07839i	−0.0758129	+	0.0437706i	−0.537427	−	0.843310i	$-0.680604\pi$
$607$	−1.86783	+	1.07839i	−0.0758129	+	0.0437706i	0.461614	+	0.887081i	$0.347270\pi$
$608$	4.53824	−	2.62015i	0.184050	−	0.106261i
$609$		0			0
$610$		0			0
$611$	−7.06804			−0.285942
$612$		0			0
$613$			9.57521i			0.386739i	0.981126	+	0.193370i	$0.0619416\pi$
$613$			9.57521i			0.386739i	−0.981126	+	0.193370i	$0.938058\pi$
$614$	30.7486	−	53.2581i	1.24091	−	2.14932i
$615$		0			0
$616$	−2.02791	−	3.51244i	−0.0817068	−	0.141520i
$617$	32.6291	−	18.8384i	1.31360	−	0.758406i	0.330907	−	0.943663i	$-0.392645\pi$
$617$	32.6291	−	18.8384i	1.31360	−	0.758406i	0.982690	+	0.185258i	$0.0593119\pi$
$618$		0			0
$619$	8.55211	−	14.8127i	0.343738	−	0.595372i	−0.641385	−	0.767219i	$-0.721640\pi$
$619$	8.55211	−	14.8127i	0.343738	−	0.595372i	0.985124	+	0.171847i	$0.0549734\pi$
$620$		0			0
$621$		0			0
$622$			19.6358i			0.787325i
$623$	10.6161	+	6.12920i	0.425324	+	0.245561i
$624$		0			0
$625$		0			0
$626$	−12.1215	−	20.9950i	−0.484471	−	0.839128i
$627$		0			0
$628$	−5.15650	−	2.97711i	−0.205767	−	0.118799i
$629$	−10.1723			−0.405595
$630$		0			0
$631$	33.1090			1.31805			0.659025	−	0.752121i	$-0.270969\pi$
$631$	33.1090			1.31805			0.659025	+	0.752121i	$0.270969\pi$
$632$	−6.57734	−	3.79743i	−0.261632	−	0.151054i
$633$		0			0
$634$	9.57500	+	16.5844i	0.380272	+	0.658650i
$635$		0			0
$636$		0			0
$637$	−5.44201	−	3.14195i	−0.215620	−	0.124489i
$638$			10.9320i			0.432800i
$639$		0			0
$640$		0			0
$641$	−11.5763	+	20.0508i	−0.457237	+	0.791957i	−0.998814	−	0.0486939i	$-0.984494\pi$
$641$	−11.5763	+	20.0508i	−0.457237	+	0.791957i	0.541577	+	0.840651i	$0.317827\pi$
$642$		0			0
$643$	−37.2944	+	21.5319i	−1.47075	+	0.849137i	−0.999461	−	0.0328430i	$-0.989544\pi$
$643$	−37.2944	+	21.5319i	−1.47075	+	0.849137i	−0.471287	+	0.881980i	$0.656211\pi$
$644$	−23.0168	−	39.8662i	−0.906988	−	1.57095i
$645$		0			0
$646$	−0.913870	+	1.58287i	−0.0359557	+	0.0622771i
$647$			20.6439i			0.811595i	0.913963	+	0.405798i	$0.133006\pi$
$647$			20.6439i			0.811595i	−0.913963	+	0.405798i	$0.866994\pi$
$648$		0			0
$649$	5.64064			0.221415
$650$		0			0
$651$		0			0
$652$	17.2638	−	9.96728i	0.676104	−	0.390349i
$653$	5.91942	−	3.41758i	0.231645	−	0.133740i	−0.379686	−	0.925116i	$-0.623968\pi$
$653$	5.91942	−	3.41758i	0.231645	−	0.133740i	0.611331	+	0.791375i	$0.290635\pi$
$654$		0			0
$655$		0			0
$656$	−0.569988			−0.0222543
$657$		0			0
$658$			92.9688i			3.62430i
$659$	13.4307	−	23.2626i	0.523184	−	0.906181i	−0.476452	−	0.879200i	$-0.658077\pi$
$659$	13.4307	−	23.2626i	0.523184	−	0.906181i	0.999636	−	0.0269806i	$-0.00858924\pi$
$660$		0			0
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	0.885915	−	0.463848i	$-0.153532\pi$
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	−0.844661	+	0.535301i	$0.820198\pi$
$662$	−13.0451	+	7.53162i	−0.507014	+	0.292725i
$663$		0			0
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$		0			0
$666$		0			0
$667$			18.5667i			0.718907i
$668$	−25.9375	−	14.9750i	−1.00355	−	0.579401i
$669$		0			0
$670$		0			0
$671$	2.58242	+	4.47288i	0.0996933	+	0.172674i
$672$		0			0
$673$	30.1553	+	17.4102i	1.16240	+	0.671112i	0.951878	−	0.306477i	$-0.0991501\pi$
$673$	30.1553	+	17.4102i	1.16240	+	0.671112i	0.210523	+	0.977589i	$0.432483\pi$
$674$	−4.76450			−0.183522
$675$		0			0
$676$	−29.5874			−1.13798
$677$	−21.3772	−	12.3421i	−0.821592	−	0.474346i	0.0293735	−	0.999569i	$-0.490649\pi$
$677$	−21.3772	−	12.3421i	−0.821592	−	0.474346i	−0.850965	+	0.525222i	$0.823982\pi$
$678$		0			0
$679$	−27.7449	−	48.0555i	−1.06475	−	1.84420i
$680$		0			0
$681$		0			0
$682$	18.7984	+	10.8532i	0.719827	+	0.415592i
$683$		−	38.4610i		−	1.47167i	−0.677162	−	0.735834i	$-0.736790\pi$
$683$		−	38.4610i		−	1.47167i	0.677162	−	0.735834i	$-0.263210\pi$
$684$		0			0
$685$		0			0
$686$	−11.4926	+	19.9057i	−0.438789	+	0.760005i
$687$		0			0
$688$	−2.25363	+	1.30114i	−0.0859190	+	0.0496054i
$689$	−1.35194	−	2.34163i	−0.0515048	−	0.0892089i
$690$		0			0
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	−0.870560	−	0.492062i	$-0.836243\pi$
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	0.861418	+	0.507896i	$0.169577\pi$
$692$		−	54.2084i		−	2.06070i
$693$		0			0
$694$	−1.47841			−0.0561197
$695$		0			0
$696$		0			0
$697$	0.210370	−	0.121457i	0.00796835	−	0.00460053i
$698$	38.5619	−	22.2637i	1.45959	−	0.842694i
$699$		0			0
$700$		0			0
$701$	18.1797			0.686637			0.343318	−	0.939219i	$-0.388449\pi$
$701$	18.1797			0.686637			0.343318	+	0.939219i	$0.388449\pi$
$702$		0			0
$703$		−	4.87614i		−	0.183907i
$704$	−7.11404	+	12.3219i	−0.268120	+	0.464398i
$705$		0			0
$706$	−10.5316	−	18.2413i	−0.396363	−	0.686520i
$707$	5.19615	−	3.00000i	0.195421	−	0.112827i
$708$		0			0
$709$	3.59355	−	6.22421i	0.134959	−	0.233755i	−0.790623	−	0.612303i	$-0.790243\pi$
$709$	3.59355	−	6.22421i	0.134959	−	0.233755i	0.925582	+	0.378548i	$0.123577\pi$
$710$		0			0
$711$		0			0
$712$			2.20257i			0.0825449i
$713$	31.9270	+	18.4331i	1.19568	+	0.690323i
$714$		0			0
$715$		0			0
$716$	2.62015	+	4.53824i	0.0979197	+	0.169602i
$717$		0			0
$718$	−55.2069	−	31.8737i	−2.06030	−	1.18952i
$719$	12.5168			0.466797			0.233399	−	0.972381i	$-0.425015\pi$
$719$	12.5168			0.466797			0.233399	+	0.972381i	$0.425015\pi$
$720$		0			0
$721$	30.7449			1.14500
$722$	33.5674	+	19.3802i	1.24925	+	0.721255i
$723$		0			0
$724$	0.550803	+	0.954019i	0.0204704	+	0.0354558i
$725$		0			0
$726$		0			0
$727$	−7.29699	−	4.21292i	−0.270631	−	0.156249i	0.358544	−	0.933513i	$-0.383273\pi$
$727$	−7.29699	−	4.21292i	−0.270631	−	0.156249i	−0.629174	+	0.777264i	$0.716607\pi$
$728$		−	1.94418i		−	0.0720562i
$729$		0			0
$730$		0			0
$731$	0.554512	−	0.960443i	0.0205094	−	0.0355233i
$732$		0			0
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	−0.105010	−	0.994471i	$-0.533487\pi$
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	0.808732	+	0.588177i	$0.200154\pi$
$734$	−7.48887	−	12.9711i	−0.276419	−	0.478772i
$735$		0			0
$736$	−19.3663	+	33.5434i	−0.713852	+	1.23643i
$737$			11.0074i			0.405463i
$738$		0			0
$739$	1.81290			0.0666887			0.0333444	−	0.999444i	$-0.489384\pi$
$739$	1.81290			0.0666887			0.0333444	+	0.999444i	$0.489384\pi$
$740$		0			0
$741$		0			0
$742$	−30.8003	+	17.7826i	−1.13072	+	0.652819i
$743$	17.4393	−	10.0686i	0.639785	−	0.369380i	−0.144747	−	0.989469i	$-0.546237\pi$
$743$	17.4393	−	10.0686i	0.639785	−	0.369380i	0.784532	+	0.620089i	$0.212903\pi$
$744$		0			0
$745$		0			0
$746$	−45.7374			−1.67457
$747$		0			0
$748$		−	4.29873i		−	0.157177i
$749$	−2.47209	+	4.28179i	−0.0903282	+	0.156453i
$750$		0			0
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	0.732834	−	0.680408i	$-0.238197\pi$
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	−0.955667	+	0.294449i	$0.904864\pi$
$752$	29.9628	−	17.2991i	1.09263	−	0.630832i
$753$		0			0
$754$	−2.62015	+	4.53824i	−0.0954203	+	0.165273i
$755$		0			0
$756$		0			0
$757$			52.9533i			1.92462i	0.271955	+	0.962310i	$0.412330\pi$
$757$			52.9533i			1.92462i	−0.271955	+	0.962310i	$0.587670\pi$
$758$	−31.4228	−	18.1419i	−1.14133	−	0.658945i
$759$		0			0
$760$		0			0
$761$	−9.22677	−	15.9812i	−0.334470	−	0.579319i	0.648913	−	0.760863i	$-0.275224\pi$
$761$	−9.22677	−	15.9812i	−0.334470	−	0.579319i	−0.983383	+	0.181543i	$0.941891\pi$
$762$		0			0
$763$	49.9105	+	28.8158i	1.80688	+	1.04320i
$764$	−47.5752			−1.72121
$765$		0			0
$766$	−0.992582			−0.0358634
$767$	2.34163	+	1.35194i	0.0845513	+	0.0488157i
$768$		0			0
$769$	−2.22677	−	3.85688i	−0.0802995	−	0.139083i	0.823079	−	0.567927i	$-0.192254\pi$
$769$	−2.22677	−	3.85688i	−0.0802995	−	0.139083i	−0.903379	+	0.428844i	$0.858921\pi$
$770$		0			0
$771$		0			0
$772$	40.5929	+	23.4363i	1.46097	+	0.843491i
$773$			38.9368i			1.40046i	0.713918	+	0.700229i	$0.246919\pi$
$773$			38.9368i			1.40046i	−0.713918	+	0.700229i	$0.753081\pi$
$774$		0			0
$775$		0			0
$776$	4.98516	−	8.63456i	0.178957	−	0.309962i
$777$		0			0
$778$	−10.0945	+	5.82806i	−0.361905	+	0.208946i
$779$	0.0582214	+	0.100842i	0.00208600	+	0.00361305i
$780$		0			0
$781$	−4.13453	+	7.16121i	−0.147945	+	0.256248i
$782$		−	13.5094i		−	0.483094i
$783$		0			0
$784$	30.7597			1.09856
$785$		0			0
$786$		0			0
$787$	29.6424	−	17.1140i	1.05664	−	0.610050i	0.132137	−	0.991231i	$-0.457816\pi$
$787$	29.6424	−	17.1140i	1.05664	−	0.610050i	0.924500	+	0.381182i	$0.124483\pi$
$788$	−31.7340	+	18.3216i	−1.13048	+	0.652681i
$789$		0			0
$790$		0			0
$791$	48.7252			1.73247
$792$		0			0
$793$			2.47580i			0.0879183i
$794$	3.91387	−	6.77902i	0.138898	−	0.240578i
$795$		0			0
$796$	−4.21564	−	7.30171i	−0.149420	−	0.258802i
$797$	−20.7547	+	11.9828i	−0.735171	+	0.424451i	−0.820311	−	0.571918i	$-0.806200\pi$
$797$	−20.7547	+	11.9828i	−0.735171	+	0.424451i	0.0851400	+	0.996369i	$0.472866\pi$
$798$		0			0
$799$	−7.37243	+	12.7694i	−0.260818	+	0.451750i
$800$		0			0
$801$		0			0
$802$		−	49.1600i		−	1.73590i
$803$	−14.4531	−	8.34452i	−0.510040	−	0.294472i
$804$		0			0
$805$		0			0
$806$	5.20257	+	9.01112i	0.183253	+	0.317403i
$807$		0			0
$808$	0.933638	+	0.539036i	0.0328453	+	0.0189632i
$809$	−0.283896			−0.00998124			−0.00499062	−	0.999988i	$-0.501589\pi$
$809$	−0.283896			−0.00998124			−0.00499062	+	0.999988i	$0.501589\pi$
$810$		0			0
$811$	32.4413			1.13917			0.569584	−	0.821933i	$-0.307104\pi$
$811$	32.4413			1.13917			0.569584	+	0.821933i	$0.307104\pi$
$812$	32.2603	+	18.6255i	1.13211	+	0.653626i
$813$		0			0
$814$	10.6103	+	18.3776i	0.371892	+	0.644136i
$815$		0			0
$816$		0			0
$817$	0.460395	+	0.265809i	0.0161072	+	0.00929948i
$818$		−	2.18710i		−	0.0764701i
$819$		0			0
$820$		0			0
$821$	20.8347	−	36.0868i	0.727136	−	1.25944i	−0.230953	−	0.972965i	$-0.574184\pi$
$821$	20.8347	−	36.0868i	0.727136	−	1.25944i	0.958089	−	0.286472i	$-0.0924824\pi$
$822$		0			0
$823$	16.7685	−	9.68130i	0.584514	−	0.337469i	−0.178412	−	0.983956i	$-0.557096\pi$
$823$	16.7685	−	9.68130i	0.584514	−	0.337469i	0.762925	+	0.646487i	$0.223763\pi$
$824$	2.76210	+	4.78410i	0.0962223	+	0.166662i
$825$		0			0
$826$	17.7826	−	30.8003i	0.618735	−	1.07168i
$827$		−	18.8097i		−	0.654076i	−0.945011	−	0.327038i	$-0.893950\pi$
$827$		−	18.8097i		−	0.654076i	0.945011	−	0.327038i	$-0.106050\pi$
$828$		0			0
$829$	33.1016			1.14967			0.574833	−	0.818271i	$-0.305067\pi$
$829$	33.1016			1.14967			0.574833	+	0.818271i	$0.305067\pi$
$830$		0			0
$831$		0			0
$832$	−5.90657	+	3.41016i	−0.204774	+	0.118226i
$833$	−11.3527	+	6.55451i	−0.393349	+	0.227100i
$834$		0			0
$835$		0			0
$836$	2.06063			0.0712682
$837$		0			0
$838$		−	54.0719i		−	1.86788i
$839$	19.8482	−	34.3781i	0.685237	−	1.18687i	−0.288125	−	0.957593i	$-0.593032\pi$
$839$	19.8482	−	34.3781i	0.685237	−	1.18687i	0.973362	−	0.229273i	$-0.0736347\pi$
$840$		0			0
$841$	6.98777	+	12.1032i	0.240958	+	0.417351i
$842$	13.8039	−	7.96969i	0.475714	−	0.274654i
$843$		0			0
$844$	17.6308	−	30.5375i	0.606878	−	1.05114i
$845$		0			0
$846$		0			0
$847$		−	37.4791i		−	1.28780i
$848$	11.4623	+	6.61775i	0.393616	+	0.227254i
$849$		0			0
$850$		0			0
$851$	18.0205	+	31.2124i	0.617734	+	1.06995i
$852$		0			0
$853$	−3.56494	−	2.05822i	−0.122061	−	0.0704722i	0.437726	−	0.899108i	$-0.355784\pi$
$853$	−3.56494	−	2.05822i	−0.122061	−	0.0704722i	−0.559788	+	0.828636i	$0.689117\pi$
$854$	32.5652			1.11436
$855$		0			0
$856$	−0.888365			−0.0303637
$857$	12.7694	+	7.37243i	0.436195	+	0.251837i	0.701982	−	0.712194i	$-0.252299\pi$
$857$	12.7694	+	7.37243i	0.436195	+	0.251837i	−0.265787	+	0.964032i	$0.585632\pi$
$858$		0			0
$859$	−18.9269	−	32.7824i	−0.645779	−	1.11852i	−0.984121	−	0.177499i	$-0.943199\pi$
$859$	−18.9269	−	32.7824i	−0.645779	−	1.11852i	0.338342	−	0.941023i	$-0.390134\pi$
$860$		0			0
$861$		0			0
$862$	14.4263	+	8.32905i	0.491363	+	0.283688i
$863$			26.7704i			0.911274i	0.890166	+	0.455637i	$0.150588\pi$
$863$			26.7704i			0.911274i	−0.890166	+	0.455637i	$0.849412\pi$
$864$		0			0
$865$		0			0
$866$	13.0508	−	22.6047i	0.443484	−	0.768137i
$867$		0			0
$868$	64.0560	−	36.9828i	2.17420	−	1.25528i
$869$	6.99258	+	12.1115i	0.237207	+	0.410855i
$870$		0			0
$871$	−2.63824	+	4.56956i	−0.0893933	+	0.154834i
$872$			10.3552i			0.350671i
$873$		0			0
$874$	6.47580			0.219047
$875$		0			0
$876$		0			0
$877$	−40.6756	+	23.4841i	−1.37352	+	0.793001i	−0.991369	−	0.131101i	$-0.958149\pi$
$877$	−40.6756	+	23.4841i	−1.37352	+	0.793001i	−0.382148	+	0.924101i	$0.624816\pi$
$878$	15.8343	−	9.14195i	0.534382	−	0.308526i
$879$		0			0
$880$		0			0
$881$	19.8055			0.667264			0.333632	−	0.942703i	$-0.391726\pi$
$881$	19.8055			0.667264			0.333632	+	0.942703i	$0.391726\pi$
$882$		0			0
$883$			6.20257i			0.208733i	0.994539	+	0.104367i	$0.0332815\pi$
$883$			6.20257i			0.208733i	−0.994539	+	0.104367i	$0.966718\pi$
$884$	1.03031	−	1.78455i	0.0346532	−	0.0600210i
$885$		0			0
$886$	3.82905	+	6.63210i	0.128639	+	0.222810i
$887$	−11.6285	+	6.71370i	−0.390446	+	0.225424i	−0.682353	−	0.731023i	$-0.739043\pi$
$887$	−11.6285	+	6.71370i	−0.390446	+	0.225424i	0.291907	+	0.956447i	$0.405710\pi$
$888$		0			0
$889$	−14.4623	+	25.0494i	−0.485049	+	0.840129i
$890$		0			0
$891$		0			0
$892$		−	63.1049i		−	2.11291i
$893$	−6.12111	−	3.53402i	−0.204835	−	0.118262i
$894$		0			0
$895$		0			0
$896$	11.8142	+	20.4628i	0.394685	+	0.683614i
$897$		0			0
$898$	−50.8972	−	29.3855i	−1.69846	−	0.980607i
$899$	−29.8325			−0.994971
$900$		0			0
$901$	−5.64064			−0.187917
$902$	−0.438860	−	0.253376i	−0.0146124	−	0.00843650i
$903$		0			0
$904$	4.37744	+	7.58196i	0.145592	+	0.252172i
$905$		0			0
$906$		0			0
$907$	−0.583325	−	0.336783i	−0.0193690	−	0.0111827i	0.490284	−	0.871563i	$-0.336893\pi$
$907$	−0.583325	−	0.336783i	−0.0193690	−	0.0111827i	−0.509653	+	0.860380i	$0.670226\pi$
$908$			3.17968i			0.105521i
$909$		0			0
$910$		0			0
$911$	−3.95485	+	6.85000i	−0.131030	+	0.226951i	−0.924074	−	0.382214i	$-0.875162\pi$
$911$	−3.95485	+	6.85000i	−0.131030	+	0.226951i	0.793044	+	0.609165i	$0.208495\pi$
$912$		0			0
$913$	−14.3523	+	8.28630i	−0.474992	+	0.274236i
$914$	36.7802	+	63.7052i	1.21658	+	2.10718i
$915$		0			0
$916$	9.68469	−	16.7744i	0.319991	−	0.554241i
$917$			24.5168i			0.809615i
$918$		0			0
$919$	8.58263			0.283115			0.141557	−	0.989930i	$-0.454789\pi$
$919$	8.58263			0.283115			0.141557	+	0.989930i	$0.454789\pi$
$920$		0			0
$921$		0			0
$922$	−62.6486	+	36.1702i	−2.06322	+	1.19120i
$923$	−3.43277	+	1.98191i	−0.112991	+	0.0652355i
$924$		0			0
$925$		0			0
$926$	15.5390			0.510644
$927$		0			0
$928$		−	31.3430i		−	1.02888i
$929$	−14.8081	+	25.6484i	−0.485838	+	0.841496i	−0.999868	−	0.0162766i	$-0.994819\pi$
$929$	−14.8081	+	25.6484i	−0.485838	+	0.841496i	0.514030	+	0.857772i	$0.328152\pi$
$930$		0			0
$931$	−3.14195	−	5.44201i	−0.102973	−	0.178355i
$932$	−17.4912	+	10.0986i	−0.572944	+	0.330789i
$933$		0			0
$934$	−31.2560	+	54.1370i	−1.02273	+	1.77142i
$935$		0			0
$936$		0			0
$937$		−	15.2058i		−	0.496753i	−0.968664	−	0.248376i	$-0.920103\pi$
$937$		−	15.2058i		−	0.496753i	0.968664	−	0.248376i	$-0.0798969\pi$
$938$	60.1053	+	34.7018i	1.96251	+	1.13305i
$939$		0			0
$940$		0			0
$941$	2.82643	+	4.89553i	0.0921391	+	0.159590i	0.908411	−	0.418078i	$-0.137296\pi$
$941$	2.82643	+	4.89553i	0.0921391	+	0.159590i	−0.816272	+	0.577668i	$0.803963\pi$
$942$		0			0
$943$	−0.745356	−	0.430332i	−0.0242721	−	0.0140135i
$944$	−13.2355			−0.430779
$945$		0			0
$946$	−2.31357			−0.0752206
$947$	−34.9841	−	20.1981i	−1.13683	−	0.656350i	−0.191187	−	0.981554i	$-0.561234\pi$
$947$	−34.9841	−	20.1981i	−1.13683	−	0.656350i	−0.945644	+	0.325204i	$0.894567\pi$
$948$		0			0
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$		0			0
$951$		0			0
$952$	−3.51244	−	2.02791i	−0.113839	−	0.0657249i
$953$		−	22.9320i		−	0.742839i	−0.928465	−	0.371419i	$-0.878871\pi$
$953$		−	22.9320i		−	0.742839i	0.928465	−	0.371419i	$-0.121129\pi$
$954$		0			0
$955$		0			0
$956$	−28.1345	+	48.7304i	−0.909936	+	1.57605i
$957$		0			0
$958$	−14.4263	+	8.32905i	−0.466094	+	0.269099i
$959$	15.2584	+	26.4283i	0.492719	+	0.853415i
$960$		0			0
$961$	−14.1177	+	24.4527i	−0.455411	+	0.788795i
$962$			10.1723i			0.327967i
$963$		0			0
$964$	14.6768			0.472708
$965$		0			0
$966$		0			0
$967$	8.98071	−	5.18501i	0.288800	−	0.166739i	−0.348601	−	0.937271i	$-0.613343\pi$
$967$	8.98071	−	5.18501i	0.288800	−	0.166739i	0.637401	+	0.770533i	$0.280010\pi$
$968$	5.83198	−	3.36710i	0.187447	−	0.108223i
$969$		0			0
$970$		0			0
$971$	−48.0410			−1.54171			−0.770854	−	0.637012i	$-0.780170\pi$
$971$	−48.0410			−1.54171			−0.770854	+	0.637012i	$0.780170\pi$
$972$		0			0
$973$		−	32.6890i		−	1.04796i
$974$	−12.4586	+	21.5789i	−0.399198	+	0.691431i
$975$		0			0
$976$	−6.05953	−	10.4954i	−0.193961	−	0.335950i
$977$	−23.4288	+	13.5266i	−0.749553	+	0.432754i	−0.825532	−	0.564355i	$-0.809125\pi$
$977$	−23.4288	+	13.5266i	−0.749553	+	0.432754i	0.0759796	+	0.997109i	$0.475792\pi$
$978$		0			0
$979$	2.02791	−	3.51244i	0.0648122	−	0.112258i
$980$		0			0
$981$		0			0
$982$			19.2355i			0.613829i
$983$	19.4697	+	11.2408i	0.620987	+	0.358527i	0.777253	−	0.629188i	$-0.216612\pi$
$983$	19.4697	+	11.2408i	0.620987	+	0.358527i	−0.156266	+	0.987715i	$0.549946\pi$
$984$		0			0
$985$		0			0
$986$	5.46598	+	9.46735i	0.174072	+	0.301502i
$987$		0			0
$988$	0.855437	+	0.493887i	0.0272151	+	0.0157126i
$989$	−3.92935			−0.124946
$990$		0			0
$991$	−26.5316			−0.842805			−0.421402	−	0.906874i	$-0.638462\pi$
$991$	−26.5316			−0.842805			−0.421402	+	0.906874i	$0.638462\pi$
$992$	−53.8967	−	31.1173i	−1.71122	−	0.987975i
$993$		0			0
$994$	26.0689	+	45.1526i	0.826855	+	1.43215i
$995$		0			0
$996$		0			0
$997$	24.5656	+	14.1829i	0.777999	+	0.449178i	0.835721	−	0.549155i	$-0.185050\pi$
$997$	24.5656	+	14.1829i	0.777999	+	0.449178i	−0.0577217	+	0.998333i	$0.518384\pi$
$998$		−	62.9433i		−	1.99243i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.k.b.424.2		12
3.2	odd	2		225.2.k.b.124.5		12
5.2	odd	4		675.2.e.b.451.3		6
5.3	odd	4		135.2.e.b.46.1		6
5.4	even	2	inner	675.2.k.b.424.5		12
9.2	odd	6		2025.2.b.l.649.2		6
9.4	even	3	inner	675.2.k.b.199.5		12
9.5	odd	6		225.2.k.b.49.2		12
9.7	even	3		2025.2.b.m.649.5		6
15.2	even	4		225.2.e.b.151.1		6
15.8	even	4		45.2.e.b.16.3	✓	6
15.14	odd	2		225.2.k.b.124.2		12
20.3	even	4		2160.2.q.k.721.3		6
45.2	even	12		2025.2.a.n.1.3		3
45.4	even	6	inner	675.2.k.b.199.2		12
45.7	odd	12		2025.2.a.o.1.1		3
45.13	odd	12		135.2.e.b.91.1		6
45.14	odd	6		225.2.k.b.49.5		12
45.22	odd	12		675.2.e.b.226.3		6
45.23	even	12		45.2.e.b.31.3	yes	6
45.29	odd	6		2025.2.b.l.649.5		6
45.32	even	12		225.2.e.b.76.1		6
45.34	even	6		2025.2.b.m.649.2		6
45.38	even	12		405.2.a.j.1.1		3
45.43	odd	12		405.2.a.i.1.3		3
60.23	odd	4		720.2.q.i.241.3		6
180.23	odd	12		720.2.q.i.481.3		6
180.43	even	12		6480.2.a.bs.1.1		3
180.83	odd	12		6480.2.a.bv.1.1		3
180.103	even	12		2160.2.q.k.1441.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.3	✓	6	15.8	even	4
45.2.e.b.31.3	yes	6	45.23	even	12
135.2.e.b.46.1		6	5.3	odd	4
135.2.e.b.91.1		6	45.13	odd	12
225.2.e.b.76.1		6	45.32	even	12
225.2.e.b.151.1		6	15.2	even	4
225.2.k.b.49.2		12	9.5	odd	6
225.2.k.b.49.5		12	45.14	odd	6
225.2.k.b.124.2		12	15.14	odd	2
225.2.k.b.124.5		12	3.2	odd	2
405.2.a.i.1.3		3	45.43	odd	12
405.2.a.j.1.1		3	45.38	even	12
675.2.e.b.226.3		6	45.22	odd	12
675.2.e.b.451.3		6	5.2	odd	4
675.2.k.b.199.2		12	45.4	even	6	inner
675.2.k.b.199.5		12	9.4	even	3	inner
675.2.k.b.424.2		12	1.1	even	1	trivial
675.2.k.b.424.5		12	5.4	even	2	inner
720.2.q.i.241.3		6	60.23	odd	4
720.2.q.i.481.3		6	180.23	odd	12
2025.2.a.n.1.3		3	45.2	even	12
2025.2.a.o.1.1		3	45.7	odd	12
2025.2.b.l.649.2		6	9.2	odd	6
2025.2.b.l.649.5		6	45.29	odd	6
2025.2.b.m.649.2		6	45.34	even	6
2025.2.b.m.649.5		6	9.7	even	3
2160.2.q.k.721.3		6	20.3	even	4
2160.2.q.k.1441.3		6	180.103	even	12
6480.2.a.bs.1.1		3	180.43	even	12
6480.2.a.bv.1.1		3	180.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80664 - 1.04307i) q^{2} +(1.17597 + 2.03684i) q^{4} +(-3.53869 - 2.04307i) q^{7} -0.734191i q^{8} +O(q^{10})\)	\(q+(-1.80664 - 1.04307i) q^{2} +(1.17597 + 2.03684i) q^{4} +(-3.53869 - 2.04307i) q^{7} -0.734191i q^{8} +(-0.675970 + 1.17081i) q^{11} +(-0.561237 + 0.324030i) q^{13} +(4.26210 + 7.38217i) q^{14} +(1.58613 - 2.74726i) q^{16} +1.35194i q^{17} -0.648061 q^{19} +(2.44247 - 1.41016i) q^{22} +(4.14827 - 2.39500i) q^{23} +1.35194 q^{26} -9.61033i q^{28} +(-1.93807 + 3.35683i) q^{29} +(3.84823 + 6.66533i) q^{31} +(-7.00279 + 4.04307i) q^{32} +(1.41016 - 2.44247i) q^{34} +7.52420i q^{37} +(1.17081 + 0.675970i) q^{38} +(-0.0898394 - 0.155606i) q^{41} +(-0.710419 - 0.410161i) q^{43} -3.17968 q^{44} -9.99258 q^{46} +(9.44526 + 5.45323i) q^{47} +(4.84823 + 8.39738i) q^{49} +(-1.32000 - 0.762100i) q^{52} +4.17226i q^{53} +(-1.50000 + 2.59808i) q^{56} +(7.00279 - 4.04307i) q^{58} +(-2.08613 - 3.61328i) q^{59} +(1.91016 - 3.30850i) q^{61} -16.0558i q^{62} +10.5242 q^{64} +(7.05113 - 4.07097i) q^{67} +(-2.75368 + 1.58984i) q^{68} +6.11644 q^{71} +12.3445i q^{73} +(7.84823 - 13.5935i) q^{74} +(-0.762100 - 1.32000i) q^{76} +(4.78410 - 2.76210i) q^{77} +(5.17226 - 8.95862i) q^{79} +0.374833i q^{82} +(10.6161 + 6.12920i) q^{83} +(0.855648 + 1.48203i) q^{86} +(0.859601 + 0.496291i) q^{88} -3.00000 q^{89} +2.64806 q^{91} +(9.75648 + 5.63290i) q^{92} +(-11.3761 - 19.7041i) q^{94} +(11.7606 + 6.79001i) q^{97} -20.2281i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4}+O(q^{10}) \) 12 * q + 10 * q^4	\( 12 q + 10 q^{4} - 4 q^{11} + 18 q^{14} - 10 q^{16} - 16 q^{19} + 8 q^{26} + 14 q^{29} - 16 q^{31} - 8 q^{34} - 26 q^{41} - 88 q^{44} - 12 q^{46} - 4 q^{49} - 18 q^{56} + 4 q^{59} - 2 q^{61} + 60 q^{64} + 40 q^{71} + 32 q^{74} + 24 q^{76} + 4 q^{79} + 56 q^{86} - 36 q^{89} + 40 q^{91} - 62 q^{94}+O(q^{100}) \) 12 * q + 10 * q^4 - 4 * q^11 + 18 * q^14 - 10 * q^16 - 16 * q^19 + 8 * q^26 + 14 * q^29 - 16 * q^31 - 8 * q^34 - 26 * q^41 - 88 * q^44 - 12 * q^46 - 4 * q^49 - 18 * q^56 + 4 * q^59 - 2 * q^61 + 60 * q^64 + 40 * q^71 + 32 * q^74 + 24 * q^76 + 4 * q^79 + 56 * q^86 - 36 * q^89 + 40 * q^91 - 62 * q^94

Introduction

L-functions

Modular forms

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Database

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